Question: Simplify the following expression: $ z = \dfrac{-7}{8} - \dfrac{-5n - 2}{-10} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10}{-10}$ $ \dfrac{-7}{8} \times \dfrac{-10}{-10} = \dfrac{70}{-80} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-5n - 2}{-10} \times \dfrac{8}{8} = \dfrac{-40n - 16}{-80} $ Therefore $ z = \dfrac{70}{-80} - \dfrac{-40n - 16}{-80} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{70 - (-40n - 16) }{-80} $ Distribute the negative sign: $z = \dfrac{70 + 40n + 16}{-80}$ $z = \dfrac{40n + 86}{-80}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{-20n - 43}{40}$